How to Find GCF of 35/20, 38/323, 460/826?

GCF of 35/20, 38/323, 460/826

Created By : Veerendra
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023

Use our free GCF of Fractions Calculator tool to compute the GCF of 35/20, 38/323, 460/826 i.e 1/2667980 easily. The following is the detailed procedure to determine the greatest common factor of fractions 35/20, 38/323, 460/826.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

What is the GCF of 35/20,38/323,460/826?

Given fractions are 35/20,38/323,460/826

To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by

GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators

In the fractions 35/20,38/323,460/826, numerators are 35,38,460

Denominators are 20,323,826

The GCF of 35,38,460 is 1 .

LCM of 20,323,826 is 2667980.

The greatest common factor of 35/20,38/323,460/826 = [GCF of 35,38,460]/[LCM of 20,323,826]= 1/2667980

Therefore, the GCF of 35/20,38/323,460/826 is 1/2667980.

Greatest Common Factor of 35,38,460

To find the highest common factor of 35,38,460, we have to find the factors of both numbers and list the highest common factor.

The factors of 35 are 1, 5, 7, 35

The factors of 38 are 1, 2, 19, 38

The factors of 460 are 1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230, 460

The HCF of 35,38,460 is 1.

Lets's calculate GCF of 35,38,460

Greatest Common Factor (GCF) of 35,38,460 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 35,38,460 By Matching Biggest Common Factor Method

Now, list down the factors of 35

1,5,7,35

Now, list down the factors of 38

1,2,19,38

Now, list down the factors of 460

1,2,4,5,10,20,23,46,92,115,230,460

Greatest Common Factor

We found the factors 35,38,460 . The biggest common factor number is the GCF number.
So the greatest common factor 35,38,460 is 1.

Lets's calculate LCM of 20,323,826

Lowest Common Multiple of 20,323,826 using Common Division

2	20, 323, 826
	10, 323, 413

∴ So the LCM of the given numbers is 2 x 10 x 323 x 413 = 2667980

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2667980

Therefore, the GCF of Fractions 35/20,38/323,460/826 is 1/2667980

Least Common Multiple of 20,323,826 with GCF Formula

The formula of LCM is LCM(a₁,a₂,a₃....,a_n) = ( a₁ × a₂ × a₃ × .... × a_n) / GCF(a₁,a₂,a₃....,a_n) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 20,323,826 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(20,323,826) = 1

common factors(in case of two or more numbers have common factors) = 2

GCF(20,323,826) x common factors =1 x 2 = 2

LCM(20,323,826) = ( 20 × 323 × 826 ) / 2

LCM(20,323,826) = 5335960 / 2

LCM(20,323,826) = 2667980

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 35/20, 38/323, 460/826

1. What is the HCF of 35,38,460?

The HCF of 35,38,460 is 1

2. What is the GCF of a fraction?

The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.

3. How to find GCF in Fractions?

Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.

4. What is the GCF of Fractions for 35/20, 38/323, 460/826?

Answer: GCF of Numerators as per given numbers 35/20, 38/323, 460/826 is

GCF of Numerators i.e. for 35,38,460 is 1

LCM of denominators i.e. for 20,323,826 is 2667980.

Thus, GCF of Fractions is 1/2667980.Finally, GCF of Fractions for 35/20, 38/323, 460/826 is 1/2667980.